Being affected by what media you are currently consuming is not an uncommon problem and, I would say, not necessarily even a bad thing. The key next step is to try to internalize the styles, to really pick them apart. Figure out what is happening on the page and why that is so effective. Start to ask the important questions:
- Why did the author choose this style over any other?
- Which elements of this style work best? Or worst?
- Which elements of this style appeal most to you? Or least?
Then write. Just write and write and write. Move around in styles and genres and mediums. Go wild. Don't worry about editing or censoring yourself. Exploration is just for you. Later, you will be able to go back and edit these pieces down to perfection. The more you write, the more you are going to find the facets that you like.
Then go back and reread what you wrote. Ask yourself the same questions you asked when reading Joyce. Parts will make you laugh or cringe or shake your head, but the best bits will be immediately apparent. A word, a phrase, a structure that just feel right to you. The kind of thing that you will want to use again.
That's your style.
I should have stated this explicitly, but this process will take many years and hard work. Part of the problem is at any given point, you will think you have found your style and you will go back to your older pieces, read them over, shake your head and mumble, "Oh man, what was I thinking?"
"Style" is an incredibly finicky thing. It's slippery. It evolves. As Patches states in his answer, your experience will inform your style. Hemingway, who has one of the most recognizable styles in literature, was not stagnant. His prose stays terse and repetitive, but it grows and refines. Between "The Sun Also Rises" (1926) and "Old Man and the Sea" (1951), he is a different person and therefore he writes differently.
That said, he thought A LOT about writing. For him, it was all there was (other than drinking and ladies and being sad...). Everything he did was largely to inform his writing. If you want to really find your style, you have to work for it. But that's the fun part.